
on Econometrics 
By:  Sid Kankanala; Victoria ZindeWalsh 
Abstract:  Kernelweighted test statistics have been widely used in a variety of settings including nonstationary regression, inference on propensity score and panel data models. We develop the limit theory for a kernelbased specification test of a parametric conditional mean when the law of the regressors may not be absolutely continuous to the Lebesgue measure and is contaminated with singular components. This result is of independent interest and may be useful in other applications that utilize kernel smoothed Ustatistics. Simulations illustrate the nontrivial impact of the distribution of the conditioning variables on the power properties of the test statistic. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.01683&r= 
By:  Rub\'en LoaizaMaya; Didier Nibbering 
Abstract:  The multinomial probit model is often used to analyze choice behaviour. However, estimation with existing Markov Chain Monte Carlo (MCMC) methods is computationally costly, which limits its applicability to large choice data sets. This paper proposes a variational inference method that is fast, even when a large number of choice alternatives and observations are considered. Variational methods usually require an analytical expression for the unnormalized posterior density and an adequate choice of variational family. Both are challenging to specify in a multinomial probit, which has a posterior that requires identifying restrictions and is augmented with a large set of latent utilities. We employ a spherical transformation on the covariance matrix of the latent utilities to construct an unnormalized augmented posterior that identifies the parameters, and use the conditional posterior of the latent utilities as part of the variational family. The proposed method is faster than MCMC, and can be made scalable to both a large numbers of choice alternatives and a large number of observations. The accuracy and scalability of our method is illustrated in numerical experiments and real purchase data with one million observations. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2202.12495&r= 
By:  Lixiong Li; Marc Henry 
Abstract:  We propose confidence regions for the parameters of incomplete models with exact coverage of the true parameter in finite samples. Our confidence region inverts a test, which generalizes Monte Carlo tests to incomplete models. The test statistic is a discrete analogue of a new optimal transport characterization of the sharp identified region. Both test statistic and critical values rely on simulation drawn from the distribution of latent variables and are computed using solutions to discrete optimal transport, hence linear programming problems. We also propose a fast preliminary search in the parameter space with an alternative, more conservative yet consistent test, based on a parameter free critical value. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.00473&r= 
By:  Fang, Qin; Guo, Shaojun; Qiao, Xinghao 
Abstract:  Statistical analysis of highdimensional functional times series arises in various applications. Under this scenario, in addition to the intrinsic infinitedimensionality of functional data, the number of functional variables can grow with the number of serially dependent observations. In this paper, we focus on the theoretical analysis of relevant estimated cross(auto)covariance terms between two multivariate functional time series or a mixture of multivariate functional and scalar time series beyond the Gaussianity assumption. We introduce a new perspective on dependence by proposing functional crossspectral stability measure to characterize the effect of dependence on these estimated cross terms, which are essential in the estimates for additive functional linear regressions. With the proposed functional crossspectral stability measure, we develop useful concentration inequalities for estimated cross(auto)covariance matrix functions to accommodate more general subGaussian functional linear processes and, furthermore, establish finite sample theory for relevant estimated terms under a commonly adopted functional principal component analysis framework. Using our derived nonasymptotic results, we investigate the convergence properties of the regularized estimates for two additive functional linear regression applications under sparsity assumptions including functional linear lagged regression and partially functional linear regression in the context of highdimensional functional/scalar time series. 
Keywords:  crossspectral stability measure; functional linear regression; functional principal component analysis; nonasymptotics; subGaussian functional linear process; sparsity; No. 11771447). 
JEL:  C1 
Date:  2022–01–10 
URL:  http://d.repec.org/n?u=RePEc:ehl:lserod:114637&r= 
By:  Martin Huber 
Abstract:  This study demonstrates the existence of a testable condition for the identification of the causal effect of a treatment on an outcome in observational data, which relies on two sets of variables, namely observed covariates to be controlled for and a suspected instrument. Under a causal structure commonly found in empirical applications, the testable conditional independence of the suspected instrument and the outcome given the treatment and the covariates has two implications. First, the instrument is valid, i.e.\ it does not directly affect the outcome (other than through the treatment) and is unconfounded conditional on the covariates. Second, the treatment is unconfounded conditional on the covariates such that the treatment effect is identified. We suggest tests of this conditional independence based on doubly robust estimators and investigate their finite sample performance in a simulation study. We also apply our testing approach to the evaluation of the impact of fertility on female labor supply when using the sibling sex ratio of the first two children as supposed instrument, which by and large points to a violation of our testable implication, at least for the moderate set of socioeconomic covariates considered. 
Date:  2022–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2203.15890&r= 
By:  Chen, Cheng; Guo, Shaojun; Qiao, Xinghao 
Abstract:  Functional linear regression is an important topic in functional data analysis. It is commonly assumed that samples of the functional predictor are independent realizations of an underlying stochastic process, and are observed over a grid of points contaminated by iid measurement errors. In practice, however, the dynamical dependence across different curves may exist and the parametric assumption on the error covariance structure could be unrealistic. In this article, we consider functional linear regression with serially dependent observations of the functional predictor, when the contamination of the predictor by the white noise is genuinely functional with fully nonparametric covariance structure. Inspired by the fact that the autocovariance function of observed functional predictors automatically filters out the impact from the unobservable noise term, we propose a novel autocovariancebased generalized methodofmoments estimate of the slope function. We also develop a nonparametric smoothing approach to handle the scenario of partially observed functional predictors. The asymptotic properties of the resulting estimators under different scenarios are established. Finally, we demonstrate that our proposed method significantly outperforms possible competing methods through an extensive set of simulations and an analysis of a public financial dataset. 
Keywords:  autocovariance; eigenanalysis; errorsinpredictors; functional linear regression; generalized methodofmoments; local linear smoothing; 11771447 
JEL:  C1 
Date:  2020–11–10 
URL:  http://d.repec.org/n?u=RePEc:ehl:lserod:114636&r= 
By:  Stefano Bertelli; Gianmarco Vacca; Maria Grazia Zoia 
Abstract:  The paper proposes a new bootstrap approach to the Pesaran, Shin and Smith's bound tests in a conditional equilibrium correction model with the aim to overcome some typical drawbacks of the latter, such as inconclusive inference and distortion in size. The bootstrap tests are worked out under several data generating processes, including degenerate cases. Monte Carlo simulations confirm the better performance of the bootstrap tests with respect to bound ones and to the asymptotic F test on the independent variables of the ARDL model. It is also proved that any inference carried out in misspecified models, such as unconditional ARDLs, may be misleading. Empirical applications highlight the importance of employing the appropriate specification and provide definitive answers to the inconclusive inference of the bound tests when exploring the longterm equilibrium relationship between economic variables. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.04939&r= 
By:  Karsten Reichold; Carsten Jentsch 
Abstract:  Traditional inference in cointegrating regressions requires tuning parameter choices to estimate a longrun variance parameter. Even in case these choices are "optimal", the tests are severely size distorted. We propose a novel selfnormalization approach, which leads to a nuisance parameter free limiting distribution without estimating the longrun variance parameter directly. This makes our selfnormalized test tuning parameter free and considerably less prone to size distortions at the cost of only small power losses. In combination with an asymptotically justified vector autoregressive sieve bootstrap to construct critical values, the selfnormalization approach shows further improvement in small to medium samples when the level of error serial correlation or regressor endogeneity is large. We illustrate the usefulness of the bootstrapassisted selfnormalized test in empirical applications by analyzing the validity of the Fisher effect in Germany and the United States. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.01373&r= 
By:  William C. Horrace (Center for Policy Research, Maxwell School, Syracuse University, 426 Eggers Hall, Syracuse, NY 13244); Hyunseok Jung (Department of Economics, University of Arkansas, Fayetteville, AR 72701); Yoonseok Lee (Center for Policy Research, Maxwell School, Syracuse University, 426 Eggers Hall, Syracuse, NY 13244) 
Abstract:  We apply the adaptive LASSO (Zou, 2006) to select a set of maximally efficient firms in the panel fixedeffect stochastic frontier model. The adaptively weighted L1 penalty with sign restrictions for firmlevel inefficiencies allows simultaneous estimation of the maximal efficiency and firmlevel inefficiency parameters, which results in a faster rate of convergence of the corresponding estimators than the leastsquares dummy variable approach. We show that the estimator possesses the oracle property and selection consistency still holds with our proposed tuning parameter selection criterion. We also propose an efficient optimization algorithm based on coordinate descent. We apply the method to estimate a group of efficient police officers who are best at detecting contraband in motor vehicle stops (i.e., search efficiency) in Syracuse, NY. 
Keywords:  Panel Data, FixedEffect Stochastic Frontier Model, Adaptive LASSO, L1 Regularization, Sign Restriction, Zero Inefficiency 
JEL:  C14 C23 D24 
Date:  2022–03 
URL:  http://d.repec.org/n?u=RePEc:max:cprwps:248&r= 
By:  Mauro Bernardi; Daniele Bianchi; Nicolas Bianco 
Abstract:  We develop a new variational Bayes estimation method for largedimensional sparse multivariate predictive regression models. Our approach allows to elicit orderinginvariant shrinkage priors directly on the regression coefficient matrix rather than a Choleskybased linear transformation, as typically implemented in existing MCMC and variational Bayes approaches. Both a simulation and an empirical study on the crossindustry predictability of equity risk premiums in the US, show that by directly shrinking weak industry interdependencies one can substantially improve both the statistical and economic outofsample performance of multivariate regression models for return predictability. This holds across alternative continuous shrinkage priors, such as the adaptive Bayesian lasso, adaptive normalgamma and the horseshoe. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2202.12644&r= 
By:  Emmet HallHoffarth 
Abstract:  This paper presents a set of tests and an algorithm for agnostic, datadriven selection among macroeconomic DSGE models inspired by structure learning methods for DAGs. As the loglinear statespace solution to any DSGE model is also a DAG it is possible to use associated concepts to identify a unique groundtruth statespace model which is compatible with an underlying DGP, based on the conditional independence relationships which are present in that DGP. In order to operationalise search for this groundtruth model, the algorithm tests feasible analogues of these conditional independence criteria against the set of combinatorially possible statespace models over observed variables. This process is consistent in large samples. In small samples the result may not be unique, so conditional independence tests can be combined with likelihood maximisation in order to select a single optimal model. The efficacy of this algorithm is demonstrated for simulated data, and results for real data are also provided and discussed. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.02374&r= 
By:  Kun Zhang; Ben Mingbin Feng; Guangwu Liu; Shiyu Wang 
Abstract:  Nested simulation is a natural approach to tackle nested estimation problems in operations research and financial engineering. The outerlevel simulation generates outer scenarios and the innerlevel simulations are run in each outer scenario to estimate the corresponding conditional expectation. The resulting sample of conditional expectations is then used to estimate different risk measures of interest. Despite its flexibility, nested simulation is notorious for its heavy computational burden. We introduce a novel simulation procedure that reuses inner simulation outputs to improve efficiency and accuracy in solving nested estimation problems. We analyze the convergence rates of the bias, variance, and MSE of the resulting estimator. In addition, central limit theorems and variance estimators are presented, which lead to asymptotically valid confidence intervals for the nested risk measure of interest. We conduct numerical studies on two financial risk measurement problems. Our numerical studies show consistent results with the asymptotic analysis and show that the proposed approach outperforms the standard nested simulation and a stateofart regression approach for nested estimation problems. 
Date:  2022–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2203.15929&r= 
By:  Manon Costa (IMT  Institut de Mathématiques de Toulouse UMR5219  INSA Toulouse  Institut National des Sciences Appliquées  Toulouse  INSA  Institut National des Sciences Appliquées  UT1  Université Toulouse 1 Capitole  Université Fédérale Toulouse MidiPyrénées  UT2J  Université Toulouse  Jean Jaurès  UT3  Université Toulouse III  Paul Sabatier  Université Fédérale Toulouse MidiPyrénées  CNRS  Centre National de la Recherche Scientifique); Sébastien Gadat (TSE  Toulouse School of Economics  UT1  Université Toulouse 1 Capitole  Université Fédérale Toulouse MidiPyrénées  EHESS  École des hautes études en sciences sociales  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) 
Abstract:  In this work, we study a new recursive stochastic algorithm for the joint estimation of quantile and superquantile of an unknown distribution. The novelty of this algorithm is to use the Cesaro averaging of the quantile estimation inside the recursive approximation of the superquantile. We provide some sharp nonasymptotic bounds on the quadratic risk of the superquantile estimator for different step size sequences. We also prove new nonasymptotic Lpcontrols on the Robbins Monro algorithm for quantile estimation and its averaged version. Finally, we derive a central limit theorem of our joint procedure using the diffusion approximation point of view hidden behind our stochastic algorithm. 
Keywords:  Stochastic approximation,Quantile and superquantile,Nonasymptotic controls,Diffusion approximation 
Date:  2021–01 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal03610477&r= 
By:  Rudy Morel; Gaspar Rochette; Roberto Leonarduzzi; JeanPhilippe Bouchaud; St\'ephane Mallat 
Abstract:  We introduce a scattering covariance matrix which provides nonGaussian models of timeseries having stationary increments. A complex wavelet transform computes signal variations at each scale. Dependencies across scales are captured by the joint covariance across time and scales of complex wavelet coefficients and their modulus. This covariance is nearly diagonalized by a second wavelet transform, which defines the scattering covariance. We show that this set of moments characterizes a wide range of nonGaussian properties of multiscale processes. This is analyzed for a variety of processes, including fractional Brownian motions, Poisson, multifractal random walks and Hawkes processes. We prove that selfsimilar processes have a scattering covariance matrix which is scale invariant. This property can be estimated numerically and defines a class of widesense selfsimilar processes. We build maximum entropy models conditioned by scattering covariance coefficients, and generate new timeseries with a microcanonical sampling algorithm. Applications are shown for highly nonGaussian financial and turbulence timeseries. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.10177&r= 
By:  Andrew Y. Chen 
Abstract:  Many scholars have called for raising statistical hurdles to guard against false discoveries in academic publications. I show these calls are unlikely to be justified empirically. Published data exhibit bias: results that fail to meet existing hurdles are often unobserved. These unobserved results must be extrapolated, leading to weak identification of revised hurdles. In contrast, statistics that can target only published findings (e.g. empirical Bayes shrinkage and the local FDR) can be strongly identified, as data on published findings is plentiful. I demonstrate these results in a general theory and in an empirical analysis of the crosssectional return predictability literature. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.10275&r= 
By:  Hamdi Ra\"issi 
Abstract:  In this paper, we propose to consider the dependence structure of the trade/no trade categorical sequence of individual illiquid stocks returns. The framework considered here is wide as constant and timevarying zero returns probability are allowed. The ability of our approach in highlighting illiquid stock's features is underlined for a variety of situations. More specifically, we show that longrun effects for the trade/no trade categorical sequence may be spuriously detected in presence of a nonconstant zero returns probability. Monte Carlo experiments, and the analysis of stocks taken from the Chilean financial market, illustrate the usefulness of the tools developed in the paper. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2203.08223&r= 
By:  Jozef Barunik; Lubos Hanus 
Abstract:  We propose a deep learning approach to probabilistic forecasting of macroeconomic and financial time series. Being able to learn complex patterns from a data rich environment, our approach is useful for a decision making that depends on uncertainty of large number of economic outcomes. Specifically, it is informative to agents facing asymmetric dependence of their loss on outcomes from possibly nonGaussian and nonlinear variables. We show the usefulness of the proposed approach on the two distinct datasets where a machine learns the pattern from data. First, we construct macroeconomic fan charts that reflect information from highdimensional data set. Second, we illustrate gains in prediction of stock return distributions which are heavy tailed, asymmetric and suffer from low signaltonoise ratio. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.06848&r= 
By:  Julia Nasiadka; Weronika Nitka; Rafa{\l} Weron 
Abstract:  We employ a recently proposed changepoint detection algorithm, the NarrowestOverThreshold (NOT) method, to select subperiods of past observations that are similar to the currently recorded values. Then, contrarily to the traditional time series approach in which the most recent $\tau$ observations are taken as the calibration sample, we estimate autoregressive models only for data in these subperiods. We illustrate our approach using a challenging dataset  dayahead electricity prices in the German EPEX SPOT market  and observe a significant improvement in forecasting accuracy compared to commonly used approaches, including the Autoregressive Hybrid Nearest Neighbors (ARHNN) method. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.00872&r= 
By:  Whitehouse, E. J. (Department of Economics, University of Sheffield, UK); Harvey, D. I. (School of Economics, University of Nottingham); Leybourne, S. J. (School of Economics, University of Nottingham) 
Abstract:  Given the financial and economic damage that can be caused by the collapse of an asset price bubble, it is of critical importance to rapidly detect the onset of a crash once a bubble has been identified. We develop a realtime monitoring procedure for detecting a crash episode in a time series. We adopt an autoregressive framework, with the bubble and crash regimes modelled by explosive and stationary dynamics respectively. The first stage of our approach is to monitor for the presence of a bubble; conditional on having detected a bubble, we monitor for a crash in real time as new data emerges. Our crash detection procedure employs a statistic based on the different signs of the means of the first differences associated with explosive and stationary regimes, and critical values are obtained using a training period, over which no bubble or crash is assumed to occur. Monte Carlo simulations suggest that our recommended procedure has a wellcontrolled false positive rate during a bubble regime, while also allowing very rapid detection of a crash when one occurs. Application to the US housing market demonstrates the efficacy of our procedure in rapidly detecting the house price crash of 2006. 
Keywords:  Realtime monitoring; Bubble; Crash; Explosive autoregression; Stationary autoregression 
JEL:  C12 C22 G01 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:shf:wpaper:2022007&r= 
By:  Yuki Oyama 
Abstract:  Although the recursive logit (RL) model has been recently popular and has led to many applications and extensions, an important numerical issue with respect to the evaluation of value functions remains unsolved. This issue is particularly significant for model estimation, during which the parameters are updated every iteration and may violate the model feasible condition. To solve this numerical issue, this paper proposes a prismconstrained RL (PrismRL) model that implicitly restricts the path set by the prism constraint defined based upon a stateextended network representation. Providing a set of numerical experiments, we show that the PrismRL model succeeds in the stable estimation regardless of the initial and true parameter values and is able to capture positive utilities. In the real application to a pedestrian network, we found the positive effect of street green presence on pedestrians. Moreover, the PrismRL model achieved higher goodness of fit than the RL model, implying that the PrismRL model can also describe more realistic route choice behavior. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.01215&r= 
By:  Todd E. Clark; Florian Huber; Gary Koop; Massimiliano Marcellino 
Abstract:  The relationship between inflation and predictors such as unemployment is potentially nonlinear with a strength that varies over time, and prediction errors error may be subject to large, asymmetric shocks. Inspired by these concerns, we develop a model for inflation forecasting that is nonparametric both in the conditional mean and in the error using Gaussian and Dirichlet processes, respectively. We discuss how both these features may be important in producing accurate forecasts of inflation. In a forecasting exercise involving CPI inflation, we find that our approach has substantial benefits, both overall and in the left tail, with nonparametric modeling of the conditional mean being of particular importance. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2202.13793&r= 
By:  HaiAnh Dang (World Bank); Peter Lanjouw (Vrije Unversiteit, Amsterdam) 
Abstract:  Measuring poverty trends and dynamics are important inputs in the formulation and design of poverty reduction policies. The empirical underpinnings of such exercises are often constrained by the absence of suitable data. We provide a broad, generalist, overview of regressionbased imputation methods that have seen widespread application to estimate poverty outcomes in datascarce environments. In particular, we review two imputation methods employed in tracking poverty over time and estimating poverty dynamics. We also discuss new areas that promise of further research. 
Keywords:  poverty, imputation, consumption, wealth index, synthetic panels, household survey 
JEL:  C15 I32 O15 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:inq:inqwps:ecineq2022611&r= 